21 May 1993 Precision of morphological estimation
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Mean-absolute-error-optimal, finite-observation, translation-invariant, binary-image filters have previously been characterized in terms of morphological representations: increasing filters as unions of erosions and nonincreasing filters as unions of hit-or-miss operators. Based upon these characterizations, (sub)optimal filters have been designed via image-process realizations. The present paper considers the precision of filter estimation via realizations. A key point: while precision deteriorates for both erosion and hit-or-miss filters as window size increases, the number of image realizations required to obtain good estimation in erosion-filter design can be much less than the number required for hit-or-miss-filter design. Thus, while in theory optimal hit-or-miss filtering is better because the unconstrained optimal hit-or-miss filter is the conditional expectation, owing to estimation error it is very possible that estimated optimal erosion filters are better than estimated optimal hit-or-miss filters.
© (1993) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Edward R. Dougherty, Edward R. Dougherty, Robert P. Loce, Robert P. Loce, } "Precision of morphological estimation", Proc. SPIE 1902, Nonlinear Image Processing IV, (21 May 1993); doi: 10.1117/12.144774; https://doi.org/10.1117/12.144774


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